On the stable equivalences between finite tensor categories

We aim to study Morita theory for tensor triangulated categories. For two finite tensor categories having no projective simple objects, we prove that their stable equivalence induced by an exact k-linear monoidal functor can be lifted to a tensor equivalence under some certain conditions.

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Yuying Xu is currently a PhD student at Nanjing University and University of Stuttgart.

Related work: "On the stable equivalences between finite tensor categories", Yuying Xu and Gongxiang Liu, Proc. Amer. Math. Soc. 151 (2023), 1867-1876

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